Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  lshpne Structured version   Unicode version

Theorem lshpne 31980
 Description: A hyperplane is not equal to the vector space. (Contributed by NM, 4-Jul-2014.)
Hypotheses
Ref Expression
lshpne.v
lshpne.h LSHyp
lshpne.w
lshpne.u
Assertion
Ref Expression
lshpne

Proof of Theorem lshpne
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 lshpne.u . . 3
2 lshpne.w . . . 4
3 lshpne.v . . . . 5
4 eqid 2402 . . . . 5
5 eqid 2402 . . . . 5
6 lshpne.h . . . . 5 LSHyp
73, 4, 5, 6islshp 31977 . . . 4
82, 7syl 17 . . 3
91, 8mpbid 210 . 2
109simp2d 1010 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   w3a 974   wceq 1405   wcel 1842   wne 2598  wrex 2754   cun 3411  csn 3971  cfv 5568  cbs 14839  clmod 17830  clss 17896  clspn 17935  LSHypclsh 31973 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4516  ax-nul 4524  ax-pr 4629 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2758  df-rex 2759  df-rab 2762  df-v 3060  df-sbc 3277  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-br 4395  df-opab 4453  df-mpt 4454  df-id 4737  df-xp 4828  df-rel 4829  df-cnv 4830  df-co 4831  df-dm 4832  df-iota 5532  df-fun 5570  df-fv 5576  df-lshyp 31975 This theorem is referenced by:  lshpnel  31981  lshpcmp  31986  lkrshp3  32104  lkrshp4  32106  dochshpncl  34384  dochlkr  34385  dochkrshp  34386  dochsatshpb  34452
 Copyright terms: Public domain W3C validator